Publications
2015
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Enhanced Visualization and Autonomous Extraction of Poincaré Map Topology.
Journal of Astronautical Sciences AAS 13-903, 2015.
(DOI: 10.1007/s40295-015-0042-4)
Abstract: Poincaré maps supply vital descriptions of dynamical behavior in spacecraft trajectory analysis,
but the puncture plot, the standard display method for maps, typically requires significant external effort
to extract topology. This investigation presents adaptations of topology-based methods to compute map
structures in multi-body dynamical environments. In particular, a scalar field visualization technique
enhances the contrast between quasi-periodic and chaotic regimes. Also, an autonomous method is outlined
to extract map topology in the planar circular restricted three-body problem. The resulting topological
skeleton supplies a network of design options through the interconnectivity of orbital structures.
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A multi-resolution interpolation scheme for pathline-based Lagrangian flow representations.
In Proc. IS&T/SPIE Electronic Imaging / Visual Data Analysis, 2015.
(DOI: 10.1117/12.2083253)
Abstract: Where the computation of particle trajectories in classic vector field representations includes
computationally involved numerical integration, a Lagrangian representation in the form of a flow map opens up
new alternative ways of trajectory extraction through interpolation. In our paper, we present a novel
reorganization of the Lagrangian representation by sub-sampling a pre-computed set of trajectories into
multiple levels of resolution, maintaining a bound over the amount of memory mapped by the file system. We
exemplify the advantages of replacing integration with interpolation for particle trajectory calculation through
a real-time, low memory cost, interactive exploration environment for the study of flow fields. Beginning with a
base resolution, once an area of interest is located, additional trajectories from other levels of resolution
are dynamically loaded, densely covering those regions of the flow field that are relevant for the extraction of
the desired feature. We show that as more trajectories are loaded, the accuracy of the extracted features
converges to the accuracy of the flow features extracted from numerical integration with the added benefit of
real-time, non-iterative, multi-resolution path and time surface extraction.
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Application of Pareto sets in quality control of series production in car manufacturing.
In Proc. IEEE Pacific Visualization Symposium, Visualization Notes, 2015.
(DOI: 10.1109/PACIFICVIS.2015.7156369)
Abstract: In car manufacturing, quality management and control are important parts of the series process. In series production, many parts are controlled in various ways in some or all stages of assembly. While tactile measurements are mostly restricted to the points on an inspection plan, this restriction does not apply to optical measurements. We propose a method based on the theory of Pareto sets (multivariate topological analysis) to cope with the large amount of data produced by optical measurements and to find points of interest on the measured surface in addition to the inspection plan. We describe a method which automatically detects areas of systematic errors on a component and visualizes them on the triangulated surface. The visualization can help experts to decide, whether a detected feature is severe enough to be added to the inspection plan.
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Visual Exploration of Location-Based Social Networks Data in Urban Planning.
In Proc. IEEE Pacific Visualization Symposium, Visualization Notes, 2015.
(DOI: 10.1109/PACIFICVIS.2015.7156367)
Abstract: The increasing amount of data generated by Location Based Social Networks (LBSN) such as Twitter, Flickr, or Foursquare, is currently drawing the attention of urban planners, as it is a new source of data that contains valuable information about the behavior of the inhabitants of a city. Making this data accessible to the urban planning domain can add value to the decision making processes. However, the analysis of the spatial and temporal characteristics of this data in the context of urban planning is an ongoing research problem. This paper describes ongoing work in the design and development of a visual exploration tool to facilitate this task. The proposed design provides an approach towards the integration of a visual exploration tool and the capabilities of a visual query system from a multilevel perspective (e.g., multiple spatial scales and temporal resolutions implicit in LBSN data). A preliminary discussion about the design and the potential insights that can be gained from the exploration and analysis of this data with the proposed tool is presented, along with the conclusions and future work for the continuation of this work.
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Contour Tree Depth Images For Large Data Visualization.
In Proc. 15th Eurographics Symposium on Parallel Graphics and Visualization (EGPGV), Cagliari, Italy, 2015.
(DOI: 10.2312/pgv.20151158)
Abstract: High-fidelity simulation models on large-scale parallel computer systems can produce data at high
computational throughput, but modern architectural trade-offs make full persistent storage to the slow I/O
subsystem prohibitively costly with respect to time. We demonstrate the feasibility and potential of combining
in situ topological contour tree analysis and compact image-based data representation to address this problem.
Our experiments show significant reductions in storage requirements using topology-guided layered depth imaging,
while preserving flexibility for explorative visualization and analysis. Our approach represents an effective
and easy-to-control trade-off between storage overhead and visualization fidelity for large data visualization.
2014
- Import of ribosomal proteins into yeast mitochondria. Biochemistry and Cell Biology, 92(6): 489-498, 2014. (DOI: 10.1139/bcb-2014-0029)
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Decomposition and Segmentation of Multivariate Data using Pareto Sets.
IEEE Transactions on Visualization and Computer Graphics 20(12):2684– 2693, 2014.
(DOI: 10.1109/tvcg.2014.2346447)
Abstract: Topological and structural analysis of multivariate data is aimed at improving the understanding and
usage of such data through identification of intrinsic features and structural relationships among multiple
variables. We present two novel methods for simplifying so-called Pareto sets that describe such structural
relationships. Such simplification is a precondition for meaningful visualization of structurally rich or noisy
data. As a framework for simplification operations, we introduce a decomposition of the data domain into regions
of equivalent structural behavior and the reachability graph that describes global connectivity of Pareto extrema.
Simplification is then performed as a sequence of edge collapses in this graph; to determine a suitable sequence
of such operations, we describe and utilize a comparison measure that reflects the changes to the data that each
operation represents. We demonstrate and evaluate our methods on synthetic and real-world examples.
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Improved Post Hoc Flow Analysis Via Lagrangian Representations.
In Proc. 4th IEEE Symposium on Large-Scale Data Analysis and Visualization (LDAV), Paris, France, 2014.
(DOI: 10.1109/LDAV.2014.7013206)
Abstract: Fluid mechanics considers two frames of reference for an observer watching a flow field: Eulerian and
Lagrangian. The former is the frame of reference traditionally used for flow analysis, and involves extracting
particle trajectories based on a vector field. With this work, we explore the opportunities that arise when
considering these trajectories from the Lagrangian frame of reference. Specifically, we consider a form where
flows are extracted in situ and then used for subsequent post hoc analysis. We believe this alternate,
Lagrangian-based form will be increasingly useful, because the Eulerian frame of reference is sensitive to
temporal frequency, and architectural trends are causing temporal frequency to drop rapidly on modern
supercomputers. We support our viewpoint by running a series of experiments, which demonstrate the Lagrangian form
can be more accurate, require less I/O, and be faster when compared to traditional advection.
2013
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Distributed Parallel Particle Advection using Work Requesting.
In Proc. IEEE Symposium on Large Data Analysis and Visualization (LDAV), 2013
(DOI: 10.1109/LDAV.2013.6675152)
Abstract: Particle advection is an important vector field visualization
technique that is difficult to apply to very large data sets in a
distributed setting due to scalability limitations in existing
algorithms. In this paper, we report on several experiments using work
requesting dynamic scheduling which achieves balanced work distribution
on arbitrary problems with minimal communication overhead. We present a
corresponding prototype implementation, provide and analyze benchmark
results, and compare our results to an existing algorithm.
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Comparative Visual Analysis of Lagrangian Transport in CFD Ensembles.
IEEE Transactions on Visualization and Computer Graphics, 19(12):2743–2752, Dec. 2013
(DOI: 10.1109/TVCG.2013.141)
Abstract: Sets of simulation runs based on parameter and model
variation, so-called ensembles, are increasingly used to model
physical behaviors whose parameter space is too large or complex to be
explored automatically. Visualization plays a key role in conveying
important properties in ensembles, such as the degree to which members
of the ensemble agree or disagree in their output. For ensembles of
time-varying vector fields, there are numerous challenges for
providing an expressive comparative visualization, among which is the
requirement to relate the effect of individual flow divergence to
joint transport characteristics of the ensemble. Yet, techniques
developed for scalar ensembles are of little use in this context, as
the notion of transport induced by a vector field cannot be modeled
using such tools. We develop a Lagrangian framework for the comparison
of flow fields in an ensemble. Our techniques evaluate individual and
joint transport variance and introduce a classification space that
facilitates incorporation of these properties into a common ensemble
visualization. Variances of Lagrangian neighborhoods are computed
using pathline integration and Principal Components Analysis. This
allows for an inclusion of uncertainty measurements into the
visualization and analysis approach. Our results demonstrate the
usefulness and expressiveness of the presented method on several
practical examples.
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GPU Acceleration of Particle Advection Workloads in a Parallel, Distributed Memory Setting.
In Proc. Eurographics Symposium on Parallel Graphics and Visualization (EGPGV), pp. 1–8, Girona, Spain, May 2013
(DOI: 10.2312/EGPGV/EGPGV13/001-008)
Abstract: Although there has been significant research in GPU acceleration, both of parallel simulation codes (i.e., GPGPU) and of single GPU visualization and analysis algorithms, there has been relatively little research devoted to visualization and analysis algorithms on GPU clusters. This oversight is significant: parallel visualization and analysis algorithms have markedly different characteristics - computational load, memory access pattern, communication, idle time, etc. - than the other two categories. In this paper, we explore the benefits of GPU acceleration for particle advection in a parallel, distributed-memory setting. As performance properties can differ dramatically between particle advection use cases, our study operates over a variety of workloads, designed to reveal insights about underlying trends. This work has a three-fold aim: (1) to map a challenging visualization and analysis algorithm - particle advection - to a complex system (a cluster of GPUs), (2) to inform its performance characteristics, and (3) to evaluate the advantages and disadvantages of using the GPU. In our performance study, we identify which factors are and are not relevant for obtaining a speedup when using GPUs. In short, this study informs the following question: if faced with a parallel particle advection problem, should you implement the solution with CPUs, with GPUs, or does it not matter?
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Cubic Gradient-Based Material Interfaces.
IEEE Transactions on Visualization and Computer Graphics 19(10):1687–1699, Oct. 2013
(DOI: 10.1109/TVCG.2013.16)
Abstract: Multi-fluid simulations often create volume fraction data,
representing fluid volumes per region or cell of a fluid data set.
Accurate and visually realistic extraction of fluid boundaries is a
challenging and essential task for efficient analysis of multi-fluid
data. In this work we present a new material interface reconstruction
method for such volume fraction data. Within each cell of the data
set, our method utilizes a gradient field approximation based on
trilinearly blended Coons-patches to generate a volume-fraction
function, representing the change in volume fractions over the cells.
A continuously varying isovalue field is applied to this function to
produce a smooth interface that preserves the given volume fractions
well. Further, the method allows user-controlled balance between
volume accuracy and physical plausibility of the interface. The method
works on two- and three-dimensional Cartesian grids, and handles
multiple materials. Calculations are performed locally and utilize
only the one-ring of cells surrounding a given cell, allowing
visualizations of the material interfaces to be easily generated on a
GPU or in a large-scale distributed parallel environment. Our results
demonstrate the robustness, accuracy and flexibility of the developed
algorithms.
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Visualization and Analysis of Vortex-Turbine Intersections in Wind Farms.
IEEE Transactions on Visualization and Computer Graphics 19(9):1579–1591, Sep. 2013
(DOI: 10.1109/TVCG.2013.18)
Abstract: Characterizing the interplay between the vortices and forces
acting on a wind turbine's blades in a qualitative and quantitative
way holds the potential for significantly improving large wind turbine
design. The paper introduces an integrated pipeline for highly
effective wind and force field analysis and visualization. We extract
vortices induced by a turbine's rotation in a wind field, and
characterize vortices in conjunction with numerically simulated forces
on the blade surfaces as these vortices strike another turbine's
blades downstream. The scientifically relevant issue to be studied is
the relationship between the extracted, approximate locations on the
blades where vortices strike the blades and the forces that exist in
those locations. This integrated approach is used to detect and
analyze turbulent flow that causes local impact on the wind turbine
blade structure. The results that we present are based on analyzing
the wind and force field data sets generated by numerical simulations,
and allow domain scientists to relate vortex-blade interactions with
power output loss in turbines and turbine life-expectancy. Our methods
have the potential to improve turbine design in order to save costs
related to turbine operation and maintenance.
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Towards High-dimensional Data Analysis in Air Quality Research.
Computer Graphics Forum 32(3):101–110, 2013.
(DOI: 10.1111/cgf.12097)
Abstract: The analysis of aerosol emission sources involves mass spectrometry data factorization, an approximation of high-dimensional data in lower-dimensional space. The optimization problem associated with this analysis is non-convex and cannot be solved optimally with currently known algorithms, resulting in factorizations with crude approximation errors that are non-accessible to scientists. We describe a new methodology for user-guided error-aware data factorization that diminishes this problem. Based on a novel formulation of factorization basis suitability and an effective combination of visualization techniques, we provide means for the visual analysis of factorization quality and local refinement of factorizations with respect to minimizing approximation errors. A case study and domain-expert evaluation by collaborating atmospheric scientists shows that our method communicates errors of numerical optimization effectively and admits the computation of high-quality data factorizations in a simple way.
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Towards Multifield Scalar Topology Based on Pareto Optimality.
Computer Graphics Forum 32(3):341–350, 2013.
(DOI: 10.1111/cgf.12121)
Abstract: How can the notion of topological structures for single scalar fields be extended to multifields? In this paper we propose a definition for such structures using the concepts of Pareto optimality and Pareto dominance. Given a set of piecewise-linear, scalar functions over a common simplicial complex of any dimension, our method finds regions of “consensus” among single fields’ critical points and their connectivity relations. We show that our concepts are useful to data analysis on real-world examples originating from fluid-flow simulations; in two cases where the consensus of multiple scalar vortex predictors is of interest and in another case where one predictor is studied under different simulation parameters. We also compare the properties of our approach with current alternatives.
2012
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On multi-scale dispersion under the influence of surface mixed layer instabilities and deep flows.
Ocean Modeling 56:16–30, 2012.
(DOI: 10.1016/j.ocemod.2012.07.004)
Abstract: A series of large eddy simulations is used to assess the transport properties of multi-scale ocean flows. In particular, we compare scale-dependent measures of Lagrangian relative dispersion and the evolution of passive tracer releases in models containing only submesoscale mixed layer instabilities and those containing mixed layer instabilities modified by deeper, baroclinic mesoscale disturbances. Visualization through 3D finite-time Lyapunov exponents and spectral analysis show that the small scale instabilities of the mixed layer rapidly lose coherence in the presence of larger-scale straining induced by the mesoscale motion. Eddy diffusivities computed from passive tracer evolution increase by an order of magnitude as the flow transitions from small to large scales. During the time period when both instabilities are present, scale-dependent relative Lagrangian dispersion, given by the finite-scale Lyapunov exponent (λ), shows two distinct plateau regions clearly associated with the disparate instability scales. In this case, the maximum value of λ over the submesocales at the surface flow is three times greater than λ at the mixed layer base which is only influenced by the deeper baroclinic motions. The results imply that parameterizations of submesoscale transport properties may be needed to accurately predict surface dispersion in models that do not explicitly resolve submesoscale turbulent features.
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Visual Steering and Verification of Mass Spectrometry Data Factorization in Air Quality Research.
IEEE Transactions on Visualization and Computer Graphics 18(12):2275–2284, 2012.
(DOI: 10.1109/TVCG.2012.280)
Abstract: The study of aerosol composition for air quality research involves the analysis of high-dimensional single particle mass spectrometry data. We describe, apply, and evaluate a novel interactive visual framework for dimensionality reduction of such data. Our framework is based on non-negative matrix factorization with specifically defined regularization terms that aid in resolving mass spectrum ambiguity. Thereby, visualization assumes a key role in providing insight into and allowing to actively control a heretofore elu- sive data processing step, and thus enabling rapid analysis meaningful to domain scientists. In extending existing black box schemes, we explore design choices for visualizing, interacting with, and steering the factorization process to produce physically meaningful results. A domain-expert evaluation of our system performed by the air quality research experts involved in this effort has shown that our method and prototype admits the finding of unambiguous and physically correct lower-dimensional basis transformations of mass spectrometry data at significantly increased speed and a higher degree of ease.
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Interactive Computation and Rendering of Finite-Time Lyapunov Exponent Fields.
IEEE Transactions on Visualization and Computer Graphics 18(8):1386–1380, 2012.
(DOI: 10.1109/TVCG.2012.33)
Abstract: Finite-time Lyapunov exponent and Lagrangian coherent structures are popular concepts in fluid dynamics for the structural analysis of fluid flows but the associated computational cost remains a major obstacle to their use in visualization. In this paper, we present a novel technique that allows for the coupled computation and visualization of salient flow structures at interactive frame rates. Our approach is built upon a hierarchical representation of the FTLE field, which is adaptively sampled and rendered to meet the need of the current visual setting. The performance of our method allows the user to explore large and complex datasets across scales and to inspect their features at arbitrary resolution. The paper discusses an efficient implementation of this strategy on the graphics hardware and provides results for an analytical flow and several CFD simulation datasets.
- Parallel Stream Surface Computation for Large Data Sets In Proc. IEEE Symposium on Large Data Analysis and Visualization (LDAV), Seatte, WA, 2012. (DOI: 10.1109/LDAV.2012.6378974)
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Analysis of Time-Dependent Flow-Sensitive PC-MRI Data.
IEEE Transactions on Visualization and Computer Graphics 18(6):966–977, 2012.
(DOI: 10.1109/TVCG.2011.80)
Abstract: Many flow visualization techniques, especially integration-based methods, are problematic when the measured data exhibits noise and discretization issues. Particularly, this is the case for flow-sensitive phase-contrast magnetic resonance imaging (PC-MRI) datasets which not only record anatomic information but also time-varying flow information. We propose a novel approach for the visualization of such datasets using integration-based methods. Our ideas are based upon finite-time Lyapunov exponents (FTLE) and enable identification of vessel boundaries in the data as high regions of separation. This allows us to correctly restrict integration-based visualization to blood vessels. We validate our technique by comparing our approach to existing anatomy-based methods as well as addressing the benefits and limitations of using FTLE to restrict flow. We also discuss the importance of parameters, i.e., advection length and data resolution, in establishing a well defined vessel boundary. We extract appropriate flow lines and surfaces that enable the visualization of blood flow within the vessels. We further enhance the visualization by analyzing flow behavior in the seeded region and generating simplified depictions.
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Volume Rendering with Multidimensional Peak Finding.
Pacific Visualization 2012, Incheon City, South Korea, 2012.
(DOI: 10.1109/PacificVis.2012.6183587)
Abstract: Peak finding provides more accurate classification for direct volume rendering by sampling directly at local maxima in a transfer function, allowing for better reproduction of high-frequency features. However, the 1D peak finding technique does not extend to higher-dimensional classification. In this work, we develop a new method for peak finding with multidimensional transfer functions, which looks for peaks along the image of the ray. We use piecewise approximations to dynamically sample in transfer function space between world-space samples. As with unidimensional peak finding, this approach is useful for specifying transfer functions with greater precision, and for accurately rendering noisy volume data at lower sampling rates. Multidimensional peak finding produces comparable image quality with order-of-magnitude better performance, and can reproduce features omitted entirely by standard classification. With no precomputation or storage requirements, it is an attractive alternative to preintegration for multidimensional transfer functions.
2011
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Visualization of Topological Structures in Area Preserving Maps.
IEEE Transactions on Visualization and Computer Graphics 17(12):1765-1774, 2011.
(DOI: 10.1109/TVCG.2011.254)
Abstract: Area-preserving maps are found across a wide range of scientific and engineering problems. Their study is made challenging by the significant computational effort typically required for their inspection but more fundamentally by the fractal complexity of salient structures. The visual inspection of these maps reveals a remarkable topological picture consisting of fixed (or periodic) points embedded in so-called island chains, invariant manifolds, and regions of ergodic behavior. This paper is concerned with the effective visualization and precise topological analysis of {area-preserving maps with two degrees of freedom} from numerical or analytical data. Specifically, a method is presented for the automatic extraction and characterization of fixed points and the computation of their invariant manifolds, also known as separatrices, to yield a complete picture of the structures present within the scale and complexity bounds selected by the user. This general approach offers a significant improvement over the visual representations that are so far available for area-preserving maps. The technique is demonstrated on a numerical simulation of magnetic confinement in a fusion reactor.
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Extracting Flow Structures Using Sparse Particles
In Proc. Vision, Modeling and Visualization Workshop '11, Berlin, Germany, 2011.
(DOI: 10.2312/PE/VMV/VMV11/153-160)
Abstract: In recent years, Lagrangian Coherent Structures (LCS) have been characterized using the Finite-Time Lyapunov Exponent, following the advection of a dense set of particles into a corresponding flow field. The large amount of particles needed to sufficiently map a flow field has been a non-trivial computational burden in the application of LCS. By seeding a minimal amount of particles into the flow field, Moving Least Squares, combined with FTLE, will extrapolate the important feature locations at which further refinement is desired. Following the refinement procedure, MLS produces a continuous function reconstruction allowing the characterization of Lagrangian Co- herent Structures with a lower number of particles. Through multiple data sets, we show that given a sparse and refined sampling, MLS will reproduce FTLE fields exhibiting a nominal error while maintaining a performance increase when compared to the standard, dense finite difference approach.
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Evaluating the Benefits of An Extended Memory Hierarchy for Parallel Streamline Algorithms.
In Proc. IEEE Symposium on Large-Scale Data Analysis and Visualization 2011, pp 57-64, Providence, RI, 2011.
(DOI: 10.1109/LDAV.2011.6092318)
Abstract: The increasing cost of achieving sufficient I/O bandwidth for high end supercomputers is leading to architectural evolutions in the I/O subsystem space. Currently popular designs create a staging area on each compute node for data output via solid state drives (SSDs), local hard drives, or both. In this paper, we investigate whether these extensions to the memory hierarchy, primarily intended for computer simulations that produce data, can also benefit visualization and analysis programs that consume data. Some algorithms, such as those that read the data only once and store the data in primary memory, can not draw obvious benefit from the presence of a deeper memory hierarchy. However, algorithms that read data repeatedly from disk are excellent candidates, since the repeated reads can be accelerated by caching the first read of a block on the new resources (i.e. SSDs or hard drives). We study such an algorithm, streamline computation, and quantify the benefits it can derive.
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Streamline Integration Using MPI-Hybrid Parallelism on a Large Multicore Architecture.
IEEE Transactions on Visualization and Computer Graphics 17(11):1702–1713, 2011.
(DOI: 10.1109/TVCG.2010.259)
Abstract: Streamline computation in a very large vector field data set represents a significant challenge due to the non-local and data-dependent nature of streamline integration. In this paper, we conduct a study of the performance characteristics of “hybrid” parallel programming and execution as applied to streamline integration on a large, multi-core platform. With multi-core processors now prevalent in clusters and supercomputers, there is a need to understand the impact of these hybrid systems in order to make the best implementation choice. We use two MPI-based distribution approaches based on established parallelization paradigms, \emph{parallelize-over-seeds} and \emph{parallelize-over-blocks}, and present a novel MPI-hybrid algorithm for each approach to compute streamlines. Our findings indicate that the work sharing between cores in the proposed MPI-hybrid parallel implementation results in much improved performance and consumes less communication and I/O bandwidth than a traditional, non-hybrid distributed implementation.
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Visualizing Invariant Manifolds in Area Preserving Maps.
Topology-Based Methods in Data Analysis and Visualization IV, R. Peikert, H. Hauser, H. Carr (eds.), Springer, to appear, 2011.
(DOI: 10.1007/978-3-642-23175-9_8)
Abstract: Area-preserving maps arise in the study of conservative dynamical systems describing a wide variety of physical phenomena, from the rotation of planets to the dynamics of a fluid. The visual inspection of these maps reveals a remarkable topological picture in which invariant manifolds form the fractal geometric scaffold of both quasi-periodic and chaotic regions. We discuss in this paper the visualization of such maps built upon these invariant manifolds. This approach is in stark contrast with the discrete Poincare plots that are typically used for the visual inspection of maps. We propose to that end several modified definitions of the finite-time Lyapunov exponents that we apply to reveal the underlying structure of the dynamics. We examine the impact of various parameters and the numerical aspects that pertain to the implementation of this method. We apply our technique to a standard analytical example and to a numerical simulation of magnetic confinement in a fusion reactor. In both cases our simple method is able to reveal salient structures across spatial scales and to yield expressive images across application domains.
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Beyond Topology: A Lagrangian Metaphor to Visualize 3D Tensor Fields
In New Developments in the Visualization and Processing of Tensor Fields, D. Laidlaw, A. Vilanova (eds.), Springer, 2012.
(DOI: 10.1007/978-3-642-27343-8_5)
Abstract: Topology was introduced in the visualization literature some 15 years ago as a mathematical language to describe and capture the salient structures of symmetric second-order tensor fields. Yet, despite significant theoretical and algorithmic advances, this approach has failed to gain wide acceptance in visualization practice over the last decade. In fact, the very idea of a versatile visualization methodology for tensor fields that could transcend application domains has been virtually abandoned in favor of problem-specific feature definitions and visual representations. We propose to revisit the basic idea underlying topology from a different perspective. To do so, we introduce a Lagrangian metaphor that transposes to the structural analysis of eigenvector fields a perspective that is commonly used in the study of fluid flows. Indeed, one can view eigenvector fields as the local superimposition of two vector fields, from which a bidirectional flow field can be defined. This allows us to analyze the structure of a tensor field through the behavior of fictitious particles advected by this flow. Specifically, we show that the separatrices of 3D tensor field topology can in fact be captured in a fuzzy and numerically more robust setting as ridges of a trajectory coherence measure. As a result, we propose an alternative structure characterization strategy for the visual analysis of practical 3D tensor fields, which we demonstrate on several synthetic and computational datasets.
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An Application of Multivariate Statistical Analysis for Query-Driven Visualization.
IEEE Transactions on Visualization and Computer Graphics 17(3):264-275, 2011.
(DOI: 10.1109/TVCG.2010.80)
Abstract: Driven by the ability to generate ever-larger, increasingly complex data, there is an urgent need in the scientific community for scalable analysis methods that can rapidly identify salient trends in scientific data. Query-Driven Visualization (QDV) strategies are among the small subset of techniques that can address both large and highly complex datasets. This paper extends the utility of QDV strategies with a statistics-based framework that integrates non-parametric distribution estimation techniques with a new segmentation strategy to visually identify statistically significant trends and features within the solution space of a query. In this framework, query distribution estimates help users to interactively explore their query’s solution and visually identify the regions where the combined behavior of constrained variables is most important, statistically, to their inquiry. Our new segmentation strategy extends the distribution estimation analysis by visually conveying the individual importance of each variable to these regions of high statistical significance. We demonstrate the analysis benefits these two strategies provide and show how they may be used to facilitate the refinement of constraints over variables expressed in a user’s query. We apply our method to datasets from two different scientific domains to demonstrate its broad applicability.
- On the computation of integral curves in adaptive mesh refinement vector fields. In H. Hagen (ed.), Scientific Visualization Seminar, Schloss Dagstuhl, Vol. 2, pp. 73-91, 2011. (DOI: 10.4230/DFU.Vol2.SciViz.2011.73)
2010
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IRIS: Illustrative Rendering for Integral Surfaces.
IEEE Transactions on Visualization and Computer Graphics, 16(6):1541–1550, 2010.
[pdf]
Abstract: Applying certain visualization techniques to datasets described on unstructured grids requires the interpolation of variables of interest at arbitrary locations within the dataset’s domain of definition. Typical solutions to the problem of finding the grid element enclosing a given interpolation point make use of a variety of spatial subdivision schemes. However, existing solutions are memory-intensive, do not scale well to large grids, or do not work reliably on grids describing complex geometries. In this paper, we propose a data structure and associated construction algorithm for fast cell location in unstructured grids, and apply it to the interpolation problem. Based on the concept of bounding interval hierarchies, the proposed approach is memory-efficient, fast and numerically robust. We examine the performance characteristics of the proposed approach and compare it to existing approaches using a number of benchmark problems related to vector field visualization. Furthermore, we demonstrate that our approach can successfully accommodate large datasets, and discuss application to visualization on both CPUs and GPUs.
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Fast, Memory-Efficient Cell Location in Unstructured Grids for Visualization.
IEEE Transactions on Visualization and Computer Graphics, 16(6):1541–1550, 2010.
[pdf]
Abstract: Applying certain visualization techniques to datasets described on unstructured grids requires the interpolation of variables of interest at arbitrary locations within the dataset’s domain of definition. Typical solutions to the problem of finding the grid element enclosing a given interpolation point make use of a variety of spatial subdivision schemes. However, existing solutions are memory-intensive, do not scale well to large grids, or do not work reliably on grids describing complex geometries. In this paper, we propose a data structure and associated construction algorithm for fast cell location in unstructured grids, and apply it to the interpolation problem. Based on the concept of bounding interval hierarchies, the proposed approach is memory-efficient, fast and numerically robust. We examine the performance characteristics of the proposed approach and compare it to existing approaches using a number of benchmark problems related to vector field visualization. Furthermore, we demonstrate that our approach can successfully accommodate large datasets, and discuss application to visualization on both CPUs and GPUs.
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Smooth, Volume-Accurate Material Interface Reconstruction.
IEEE Transactions on Visualization and Computer Graphics, 16(5):802–814, 2010.
[pdf]
Abstract: A new material interface reconstruction method for volume fraction data is presented. Our method is comprised of two components: first, we generate initial interface topology; then, using a combination of smoothing and volumetric forces w ithin an active interface model, we iteratively transform the initial material interfaces into high-quality surfaces that accurately approximate the problem’s volume fractions. Unlike all previous work, our new method produces material interfaces that are smooth, co ntinuous across cell boundaries, and segment cells into regions with proper volume. These properties are critical during visualizatio n and analysis. Generating high-quality mesh representations of material interfaces is required for accurate calculations of interfac e statistics, and dramatically increases the utility of material boundary visualizations.
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Direct Visualization of Fiber Information by Coherence.
International Journal of Computer Assisted Radiology and Surgery 5(2):125–131, 2010.
[pdf]
Abstract: We present a method for visualization and analysis of three-dimensional tensor data based on a coherence measure defined on fiber tracts. This quantitative assessment is based on infinitesimal deviations of neighboring integral lines and allows identification and classification of regions with coherent fiber behavior as well as the detection of the incoherent behavior occurring at the interface between distinct regions. With this approach, we are able to extract and visualize important structures of typical tensor data sets in medical applications. We use a hardware-accelerated implementation that is capable of computing sweeping plane representations at interactive frame rates and extract volumetric information suitable, e.g. for filtering or volume-rendering, within seconds. We provide a GPU-accelerated implementation that is capable of computing sweeping plane representations at interactive frame rates and extract volumetric information within seconds. We demonstrate our method and examine its properties on datasets from medial applications.
- Recent Advances in VisIt: AMR Streamlines and Query-Driven Visualization. Numerical Modeling of Space Plasma Flows: Astronum 2009 (Astronomical Society of the Pacific Conference Series), Vol. 429, pp. 329-334, 2010. [pdf]
2009
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Time and Streak Surfaces for Flow Visualization in Large Time-Varying Data Sets.
IEEE Transactions on Visualization and Computer Graphics, 15(6):1267–1274, 2009.
[pdf]
Abstract: Time and streak surfaces are ideal tools to illustrate time-varying vector fields since they directly appeal to the intuition about coherently moving particles. However, efficient generation of high-quality time and streak surfaces for complex, large and time-varying vector field data has been elusive due to the computational effort involved. In this work, we propose a novel algorithm for computing such surfaces. Our approach is based on a decoupling of surface advection and surface adaptation and yields improved efficiency over other surface tracking methods, and allows us to leverage inherent parallelization opportunities in the surface advection, resulting in more rapid parallel computation. Moreover, we obtain as a result of our algorithm the entire evolution of a time or streak surface in a compact representation, allowing for interactive, high-quality rendering, visualization and exploration of the evolving surface. Finally, we discuss a number of ways to improve surface depiction through advanced rendering and texturing, while preserving interactivity, and provide a number of examples for real-world datasets and analyze the behavior of our algorithm on them.
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Scalable Computation of Streamlines on Very Large Datasets
In Proc. Supercomputing ‘09, Portland, OR, November, 2009.
[pdf]
Abstract: Understanding vector fields resulting from large scientific simulations is an important and often difficult task. Streamlines, curves that are tangential to a vector field at each point, are a powerful visualization method in this context. Application of streamline-based visualization to very large vector field data represents a significant challenge due to the non-local and data-dependent nature of streamline computation, and requires careful balancing of computational demands placed on I/O, memory, communication, and processors. In this paper we review two parallelization approaches based on established parallelization paradigms (static de- composition and on-demand loading) and present a novel hybrid algorithm for computing streamlines. Our algorithm is aimed at good scalability and performance across the widely varying computational characteristics of streamline- based problems. We perform performance and scalability studies of all three algorithms on a number of prototypical application problems and demonstrate that our hybrid scheme is able to perform well in different settings.
- FAnToM - Lessons Learned from Design, Implementation, Administration, and Use of a Visualization System for Over 10 Years. In Proc. Refactoring Visualization from Experience (ReVisE) 2009, Atlantic City, NJ. Oct 2009.
- Occam's Razor and Petascale Visual Data Analysis Journal of Physics: Conference Series, Vol. 180, p. 012084, 2009.
- Twists and Turns: Vector Field Visual Data Analysis Technologies for Petascale Computational Science. SciDAC Review 15, November 2009.
2008
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Generation of Accurate Integral Surfaces in Time-Dependent Vector Fields
In IEEE Transactions on Visualization and Computer Graphics, 14(6):1404–1411, 2008.
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Abstract: We present a novel approach for the direct computation of integral surfaces in time-dependent vector fields. As opposed to previous work, which we analyze in detail, our approach is based on a separation of integral surface computation into two stages: surface approximation and generation of a graphical representation. This allows us to overcome several limitations of existing techniques. We first describe an algorithm for surface integration that approximates a series of time lines using iterative refinement and computes a skeleton of the integral surface. In a second step, we generate a well-conditioned triangulation. Our approach allows a highly accurate treatment of very large time-varying vector fields in an efficient, streaming fashion. We examine the properties of the presented methods on several example datasets and perform a numerical study of its correctness and accuracy. Finally, we investigate some visualization aspects of integral surfaces.
- Topological Methods for Visualizing Vortical Flows. Mathematical Foundations of Visualization, Computer Graphics, and Massive Data Exploration, Springer, 2008.
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On the Role of Domain-specific Knowledge in the Visualization of Technical Flows
In Proceedings of Simulation and Visualization 2008, pp 107-120, Magdeburg 2008.
[pdf]
Abstract: In this paper, we present an overview of a number of existing flow visualization methods, developed by the authors in the recent past, that are specifically aimed at integrating and leveraging domain-specific knowledge into the visualization process. These methods transcend the traditional divide between interactive exploration and feature- based schemes and allow a visualization user to benefit from the abstraction properties of feature extraction and topological methods while retaining intuitive and interactive control over the visual analysis process, as we demonstrate on a number of examples.
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Lagrangian Visualization of Flow Embedded Surface Structures
In Computer Graphics Forum 27(3):1007-1014, 2008.
[pdf]
Abstract: The notions of Finite-Time Lyapunov Exponent (FTLE) and Lagrangian Coherent Structures provide a strong framework for the analysis and visualization of complex technical flows. Their definition is simple and intuitive, and they are built on a deep theoretical foundation. We apply these concepts to enable the analysis of flows in the immediate vicinity of the boundaries of flow-embedded objects by limiting the Lagrangian analysis to surfaces closely neighboring these boundaries. To this purpose, we present an approach to approximate FTLE fields over such surfaces. Furthermore, we achieve an effective depiction of boundary-related flow structures such as separation and attachment over object boundaries and specific insight into the surrounding flow using several specifically chosen visualization techniques. We document the applicability of our methods by presenting a number of application examples.
- Applications of Texture-Based Flow Visualization. In Engineering Applications of Computational Fluid Mechanics, 2(3):264–274, 2008. [pdf]
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Pathline Predicates and Unsteady Flow Structures.
The Visual Computer: International Journal of Computer Graphics, 24(12):1039–1051, 2008.
[pdf]
Abstract: We present a flow analysis framework based on pathline predicates. Such predicates are Boolean functions defined on pathlines that decide if a given pathline has a property of interest to the user. We show that any suitable set of pathline predicates can be interpreted as an unsteady flow structure definition. The visualization of the resulting unsteady flow structure provides a visual description of overall flow behavior with respect to the user’s interest. Furthermore, this flow structure serves as a basis for pathline seeding tailored to the requirements of specific visualization problems.
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Discrete Multi-Material Interface Reconstruction for Volume Fraction Dat
In Computer Graphics Forum (Proc. Eurographics/IEEE-VGTC Symposium on Visualization 2008), 27(3):1015–1022, 2008.
[pdf]
Abstract: Material interface reconstruction (MIR) is the task of constructing boundary interfaces between regions of homogeneous material, while satisfying volume constraints, over a structured or unstructured spatial domain. In this paper, we present a discrete approach to MIR based upon optimizing the labeling of fractional volume elements within a discretization of the problem's original domain. We detail how to construct and initially label a discretization, and introduce a \emph{volume conservative swap} move for optimization. Furthermore, we discuss methods for extracting and visualizing material interfaces from the discretization. Our technique has significant advantages over previous methods: we produce interfaces between multiple materials that are continuous across cell boundaries for time-varying and static data in arbitrary dimension with bounded error.
- Seeing the Unseeable. SciDAC Review, Nr. 8, pp. 24-33, 2008.
2007
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Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications.
In IEEE Transactions on Visualization and Computer Graphics (Proc. IEEE Visualization), 13(6):1464–1471, 2007.
[pdf]
Abstract: The recently introduced notion of Finite-Time Lyapunov Exponent to characterize Coherent Lagrangian Structures provides a powerful framework for the visualization and analysis of complex technical flows. Its definition is simple and intuitive, and it has a deep theoretical foundation. While the application of this approach seems straightforward in theory, the associated computational cost is essentially prohibitive. Due to the Lagrangian nature of this technique, a huge number of particle paths must be computed to fill the space-time flow domain. In this paper, we propose a novel scheme for the adaptive computation of FTLE fields in two and three dimensions that significantly reduces the number of required particle paths. Furthermore, for three-dimensional flows, we show on several examples that meaningful results can be obtained by restricting the analysis to a well-chosen plane intersecting the flow domain. Finally, we examine some of the visualization aspects of FTLE-based methods and introduce several new variations that help in the analysis of specific aspects of a flow.
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Listener-based Analysis of Surface Importance for Acoustic Metrics
In IEEE Transactions on Visualization and Computer Graphics (Proc. IEEE Visualization), 13(6):1680–1687, 2007.
[pdf]
Abstract: Acoustic quality in room acoustics is measured by well defined quantities, like definition, which can be derived from simulated impulse response filters or measured values. These take into account the intensity and phase shift of multiple reflections due to a wave front emanating from a sound source. Definition (D50) and clarity (C50) for example correspond to the fraction of the energy received in total to the energy received in the first 50 ms at a certain listener position. Unfortunately, the impulse response measured at a single point does not provide any information about the direction of reflections, and about the reflection surfaces which contribute to this measure. For the visualization of room acoustics, however, this information is very useful since it allows to discover regions with high contribution and provides insight into the influence of all reflecting surfaces to the quality measure. We use the phonon tracing method to calculate the contribution of the reflection surfaces to the impulse response for different listener positions. This data is used to compute importance values for the geometry taking a certain acoustic metric into account. To get a visual insight into the directional aspect, we map the importance to the reflecting surfaces of the geometry. This visualization indicates which parts of the surfaces need to be changed to enhance the chosen acoustic quality measure. We apply our method to the acoustic improvement of a lecture hall by means of enhancing the overall speech comprehensibility (clarity) and evaluate the results using glyphs to visualize the clarity (C50) values at listener positions throughout the room.
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Moment Invariants for the Analysis of 2D Flow Fields.
In IEEE Transactions on Visualization and Computer Graphics (Proc. IEEE Visualization), 13(6):1743–1750, 2007.
[pdf]
Abstract: We present a novel approach for analyzing two-dimensional (2D) flow field data based on the idea of invariant moments. Moment invariants have traditionally been used in computer vision applications, and we have adapted them for the purpose of interactive exploration of flow field data. The new class of moment invariants we have developed allows us to extract and visualize 2D flow patterns, invariant under translation, scaling, and rotation. With our approach one can study arbitrary flow patterns by searching a given 2D flow data set for any type of pattern as specified by a user. Further, our approach supports the computation of moments at multiple scales, facilitating fast pattern extraction and recognition. This can be done for critical point classification, but also for patterns with greater complexity. This multi-scale moment representation is also valuable for the comparative visualization of flow field data. The specific novel contributions of the work presented are the mathematical derivation of the new class of moment invariants, their analysis regarding critical point features, the efficient computation of a novel feature space representation, and based upon this the development of a fast pattern recognition algorithm for complex flow structures.
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Computation of Localized Flow for Steady and Unsteady Vector Fields and its Applications
In IEEE Transactions on Visualization and Computer Graphics 13(4):641–651, 2007.
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Abstract: We present, extend and apply a method to extract the contribution of a subregion of a data set to the global flow. To isolate this contribution we decompose the flow in the subregion into a potential flow that is induced by the original flow on the boundary and a localized flow. The localized flow is obtained by subtracting the potential flow from the original flow. Since the potential flow is free of both divergence and rotation the localized flow retains the original features and captures the region-specific flow that contains the local contribution of the considered sub- domain to the global flow. In the remainder of the paper, we describe an implementation on unstructured grids in both two and three dimensions for steady and unsteady flow fields. We discuss the application of some widely used feature extraction methods on the localized flow and describe applications like reverse-flow detection using the potential flow. Finally, we show that our algorithm is robust and scalable by applying it to various flow data sets and giving performance figures.
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Interactive Visualization of Coherent Structures in Transient Flows.
In Proc. of Topology-based Methods in Visualization, Mathematics+Visualization, Springer, 2007.
[pdf]
Abstract: In this paper we leverage a concept called Finite-Time Lyapunov Exponent (FTLE) that has its roots in dynamical systems theory and has been recently introduced in the fluid dynamics community to resolve this ambiguity. To that end we propose to combine the visual effectiveness of texture-based representations with the physically intuitive meaning of the coherent Lagrangian structures characterized by FTLE. Our method leverages the performance of the Graphics Processing Unit (GPU) to accelerate computation of FTLE and to create expressive animations of the flow that the user can interactively adjust to fit the needs of his visual analysis. We present the application of this approach to the visualization of different transient flows obtained through Direct Navier-Stokes simulations and investigate the combination of FTLE visualization with other unsteady visualization methods such as GPUFLIC.
2006
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GPU-based Simulation of Cold Air Flow for Environmental Planning.
In Proc. Spring Conference on Computer Graphics (SCCG) 2006.
[pdf]
Abstract: Simulating the effects of different land-use types regarding flow resistance and cold air production is important for controlling air quality around urban areas. In this paper we present a mathematical model and a simulation method for this problem. This model describes the cold air flow to be composed of two variables. The first is the velocity field which depends on flow resistance and the flow gradient. The second variable is a height field of the cold air which depends on cold air production and advection. To accelerate the simulation and its visualization, it is adapted to run on a GPU(Graphical Processing Unit). Implementing the simulation on fragment shaders makes it possible to combine the height field of the landscape with a color-coded volume rendering of the associated cold-air height. In two passes we compute the cold air height for each time step and render the result to a texture. In a third pass, we render the height field of the landscape using this texture as multi-layered opacity map.
- Stream Surfaces and Texture Advection: A Hybrid Metaphor for Visualization of CFD Simulation Results. In Proc. 12th International Symposium on Flow Visualization (ISFV12), Göttingen, Germany, 2006.
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Texture Advection on Stream Surfaces: A Novel Hybrid Visualization Applied to CFD Simulation Results.
In Proc. Joint EUROGRAPHICS - IEEE VGTC Symposium on Visualization (EuroVis), 2006.
[pdf]
Abstract: Stream surfaces are a classic flow visualization technique used to portray the characteristics of vector fields, and texture advection research has made rapid advances in recent years. We present a novel hybrid visualization of texture advection on stream surfaces. This approach conveys properties of the vector field that stream surfaces alone cannot. We apply the visualization technique to various patterns of flow from CFD data important to automotive engine simulation including two patterns of in-cylinder flow (swirl and tumble motion) as well as flow through a cooling jacket. In addition, we explore multiple vector fields defined at the stream surface such as velocity, vorticity, and pressure gradient. The results of our investigation highlight both the strengths and limitations of the hybrid stream surface-texture advection visualization technique and offer new insight to engineers exploring and analyzing their simulations.
- Topological Methods for Visualizing Vortical Flows. In Mathematical Foundations of Visualization, Computer Graphics, and Massive Data Exploration, Mathematics+Visualization, Springer, 2006. [pdf]
2005
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Topology-Based Flow Analysis and Superposition Effects.
In Proc. Topology-based Methods in Visualization, Mathematics+Visualization, Springer, 2005.
[pdf]
Abstract: Using topology for feature analysis in flow fields faces several problems. First of all, not all features can be detected using topology based methods. Second, while in flow feature analysis the user is interested in a quantification of feature parameters like position, size, shape, radial velocity and other parameters of feature models, many of these parameters can not be determined using topology based methods alone. Additionally, in some applications it is advantageous to regard the vector field as a superposition of several, possibly simple, features. As topology based methods are quite sensitive to superposition effects, their precision and usability is limited in these cases. In this paper, topology based analysis and visualization of flow fields is estimated and compared to other feature based approaches demonstrating these problems.
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Localized Flow Analysis of 2D and 3D Vector Fields.
In Proc. of Joint Eurographics/IEEE-VGTC Symposium on Visualization (EuroVis), 2005.
[pdf]
Abstract: In this paper we present an approach to the analysis of the contribution of a small subregion in a dataset to the global flow. To this purpose, we subtract the potential flow that is induced by the boundary of the sub-domain from the original flow. Since the potential flow is free of both divergence and rotation, the localized flow field retains the original features. In contrast to similar approaches, by making explicit use of the boundary flow of the subregion, we manage to isolate the region-specific flow that contains exactly the local contribution of the considered subdomain to the global flow. In the remainder of the paper, we describe an implementation on unstructured grids in both two and three dimensions. We discuss the application of several widely used feature extraction methods on the localized flow, with an emphasis on topological schemes.
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Visual Analysis and Exploration of Fluid Flow in a Cooling Jacket.
In Proc. IEEE Visualization 2005, Minneapolis, MS.
[pdf]
Abstract: We present a visual analysis and exploration of fluid flow through a cooling jacket. Engineers invest a large amount of time and serious effort to optimize the flow through this engine component be- cause of its important role in transferring heat away from the engine block. In this study we examine the design goals that engineers apply in order to construct an ideal-as-possible cooling jacket geometry and use a broad range of visualization tools in order to analyze, explore, and present the results. We systematically employ direct, geometric, and texture-based flow visualization techniques as well as automatic feature extraction and interactive feature-based methodology. And we discuss the relative advantages and disadvantages of these approaches as well as the challenges, both technical and perceptual with this application. The result is a feature-rich state-of-the-art flow visualization analysis applied to an important and complex data set from real-world computational fluid dynamics simulations.
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Extraction and Visualization of Swirl and Tumble Motion from Engine Simulation Data.
In Topology-based Methods in Visualization, Mathematics+Visualization, Springer, 2005.
[pdf]
Abstract: Optimizing the combustion process within an engine block is central to the performance of many motorized vehicles. Associated with this process are two important patterns of flow: swirl and tumble motion, which optimize the mixing of fluid within each of an engine's cylinders. Good visualizations are necessary to analyze the simulation data of these in-cylinder flows. We present a range of methods including integral, feature-based, and image-based schemes with the goal of extracting and visualizing these two important patterns of motion. We place a strong emphasis on automatic and semi-automatic methods that require little or no user input. The simulation data associated with in-cylinder tumble motion within a gas engine, given on an unstructured, time-varying and adaptive resolution CFD grid, demands robust visualization methods that apply to unsteady flow. We make effective use of animation to visualize the time-dependent simulation data. We also describe the challenges and implementation measures necessary in order to apply the presented methods to time-varying, volumetric grids.
- Fast and Robust Extraction of Separation Line Features.. In Scientific Visualization: The Visual Extraction of Knowledge from Data, G.-P. Bonneau, T. Ertl, and G.M. Nielson (eds.), pp. 249–264, Springer, 2005. [pdf]
- An Introduction to Linear Algebra. Visualization and Processing of Tensor Fields, Mathematics+Visualization, Springer, 2005.
2004
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Visualization of Intricate Flow Structures for Vortex Breakdown Analysis.
In Proc.
IEEE Visualization 2004, pp. 187-194.
[pdf]
Abstract: Vortex breakdowns and flow recirculation are essential phenomena in aeronautics where they appear as a limiting factor in the design of modern aircrafts. Because of the inherent intricacy of these features, standard flow visualization techniques typically yield clut- tered depictions. The paper addresses the challenges raised by the visual exploration and validation of two CFD simulations involving vortex breakdown. To permit accurate and insightful visualization we propose a new approach that unfolds the geometry of the break- down region by letting a plane travel through the structure along a curve. We track the continuous evolution of the associated pro- jected vector field using the theoretical framework of parametric topology. To improve the understanding of the spatial relationship between the resulting curves and lines we use direct volume rendering and multi-dimensional transfer functions for the display of flow-derived scalar quantities. This enriches the visualization and provides an intuitive context for the extracted topological informa- tion. Our results offer clear, synthetic depictions that permit new insight into the structural properties of vortex breakdowns.
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Tracking of Vector Field Singularities in Unstructured 3D Time-Dependent Data Sets.
In Proc. IEEE Visualization 2004, pp. 329-336.
[pdf]
Abstract: In this paper, we present an approach for monitoring the positions of vector field singularities in time-dependent datasets. The concept of singularity index is discussed and extended from the well-understood planar case to the more intricate three-dimensional setting. Assuming a tetrahedral grid with linear interpolation in space and time, vector field singularities obey rules imposed by fundamental invariants (Poincaré index), which we use as a basis for an efficient tracking algorithm. We apply the presented algorithm to CFD datasets to illustrate its purpose in the examination of structures that exhibit topological variations with time and describe some of the insight gained with this method. We give examples that show a correlation in the evolution of physical quantities that constitute to vortex breakdown.
- Accurate and Efficient Visualization of Flow Structures in a Delta Wing Simulation. In. Proc. 34th AIAA Fluid Dynamics Conference and Exhibit, 2004, AIAA paper #2004-2153.
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Surface Techniques for Vortex Visualization.
In Proc. Joint Eurographics-IEEE TCVG Symposium on Visualization Proceedings (VisSym), pp. 155-164, 2004.
[pdf]
Abstract: This paper presents powerful surface based techniques for the analysis of complex flow fields resulting from CFD simulations. Emphasis is put on the examination of vortical structures. An improved method for stream surface computation that delivers accurate results in regions of intricate flow is presented, along with a novel method to determine boundary surfaces of vortex cores. A number of surface techniques are presented that aid in understanding the flow behavior displayed by these surfaces. Furthermore, a scheme for phenomenological extraction of vortex core lines using stream surfaces is discussed and its accuracy is compared to one of the most established standard techniques.